plot() no longer fails on a sample size object when
type = "power_curve" is requested. The reference-line block
selected its branch on the presence of an n2 column, which
both object shapes have, so a sample size object entered the branch
written for power objects and read a powerCoprimary column
that is not there. The branches now select on
powerCoprimary, which distinguishes the two shapes, and the
branch already written for sample size objects is reachable for the
first time.
plot() no longer fails on a power object when
type = "sample_size_rho" is requested. A power object
carries neither the allocation ratio r, the type II error
rate beta nor the total N. These are now
derived from the columns it does carry: the realized allocation
n1 / n2, the achieved power as the target, and the sum of
the two group sizes.
plot() no longer fails on results from
ss2BinaryExact() and power2BinaryExact(). The
plotting helpers passed the object’s Test value into the
approximate binary functions, which do not accept the exact test names,
so the default call failed for every exact test. The helpers now route
exact test names to power2BinaryExact() and
ss2BinaryExact().
power2BinaryApprox() now validates
Test. An unrecognized value previously fell through every
branch and the function failed with an internal error about a missing
object instead of a message naming the valid values.
ss2MixedCountContinuous() now requires
r1 < r2 and mu1 < mu2. Treatment benefit
on both endpoints is a lower value, so with the effects reversed the
power decreases as the sample size grows, no sample size attains the
target, and the sequential search did not terminate.
power2Continuous() with
known_var = FALSE now returns zero power when
n1 + n2 - 2 < 1 instead of failing inside
rWishart(). The variance cannot be estimated from fewer
than three patients, so the t-test does not exist.
ss2Continuous(known_var = FALSE) previously failed for
standardized effect sizes above about 4 for this reason.
plot() on a result from
ss1Continuous(), ss1Count() or
ss1BinaryApprox() now explains that the co-primary plot
methods need a two-endpoint result, rather than reporting that the
endpoint type could not be determined.
ss1BinaryApprox() returns the smallest sample size
at which power2BinaryApprox() attains the target power, for
all four asymptotic methods. The closed-form expression is kept only as
the starting value of the sequential search, so the size returned and
the power reported by the package can no longer disagree. Four faults
are removed by the change. The arcsine multiplier was
(1 + kappa) / kappa, the form written for
kappa = n1 / n2, while the function defines
kappa = n2 / n1, so at r = 2 the function
returned roughly twice the required sample size. The "ASc"
continuity correction moved the two groups apart rather than toward each
other, so it reduced the sample size below the uncorrected value. The
corrected methods "ANc" and "ASc" solved their
fixed point by an iteration that stopped once two successive values
differed by one, which can return a size that does not satisfy its own
correction and can cycle without terminating, for instance at
p1 = 0.95, p2 = 0.05 and r = 5.
And the "ASc" variance was 1 / (4 n) rather
than the corrected-proportion form of Sozu et al. (2012), Supporting
Information Table 1, which the power function uses; the two disagreed
for about half of the designs of that table. The twelve published
"ANc" and "ASc" single-endpoint sizes of Table
S5 are now reproduced exactly.
ss1BinaryApprox(Test = "Fisher") steps back down
after its upward search, so the size returned is the smallest one
attaining the target power rather than the first one reached from the
starting value.
power2BinaryApprox(Test = "ASc") returns zero power
where the continuity correction carries a probability out of
(0, 1), which happens at the smallest sample sizes. The
corrected variance then vanished or was negative, and the reported power
was one half or NaN.
power2BinaryApprox() evaluates the co-primary power
at the Frechet bounds of its two marginals when the correlation between
the test statistics reaches plus or minus one, rather than calling the
bivariate normal distribution function at a correlation it does not
accept. The power is the smaller marginal at plus one and the Bonferroni
bound at minus one.
power2MixedContinuousBinary(Test = "ASc") gains the
same guard on the corrected proportions, and its "Fisher"
branch returns zero power when n1 + n2 - 2 < 1 rather
than dividing by zero degrees of freedom.
power2Continuous() validates its arguments. It
previously accepted a negative standard deviation, a group size of zero
and a non-integer group size, and returned a number for each.
dbibinom() returns the comonotone limit at the upper
Prentice bound when the two marginal probabilities are equal. The
dependence parameter of the bivariate binomial distribution diverges
there and the returned masses were NaN.
ss1Count() requires r1 < r2. With
the two rates reversed the power decreases as the sample size grows, so
no sample size attains the target.
rr1Binary(Test = "Z-pool") and
rr1Binary(Test = "Boschloo") build the rejection region
when a group has a single subject. Only one distinct value of the
ordering statistic is then ordered, and the grid of null probabilities
was simplified from a matrix to a vector, so the function failed with an
error about an incorrect number of dimensions.
plot(type = "effect_contour") grids standardized
effect sizes, which is what its axis labels state. It previously used a
grid of mean differences and labeled them as standardized, so the
contours were misplaced for any standard deviation other than one. The
marked point is now on the same scale.
plot(type = "power_curve") no longer inverts its
default window for a design of fewer than twenty per group. The lower
end of the window was a fixed floor of ten, above the upper end for a
small design.
design_table() now forwards nMC to the
mixed continuous-binary functions. The argument was documented and
honored for continuous endpoints but silently ignored on that path,
which ran at the default of 10000 in the function it calls.
The sequential search no longer adds one back to n2
when the downward search stops at n2 = 1 with the power
still at or above target.
design_table() uses seq_len() over the
parameter grid, so a zero-row grid no longer iterates.
power2BinaryApprox() now validates n1,
n2, the four probabilities and alpha, as
power2BinaryExact() already did. A group size of zero or a
probability outside the unit interval previously returned a number
rather than a message.
corrbound2MixedCountContinuous() no longer depends
on mu or sd. The bounds are a correlation,
which is invariant to the location and the scale of the continuous
endpoint, but they were computed by a quadrature over the whole real
line in the untransformed variable. That quadrature returns zero when
the mean lies far from the origin relative to the standard deviation: at
mu of -50 and sd of 0.5 both bounds collapsed
to zero, and power2MixedCountContinuous() and
ss2MixedCountContinuous() then refused every correlation,
zero included. The integrals are taken in the standardized variable
instead.
power2Continuous(known_var = FALSE) returns a power
for a design of three patients in total. rWishart()
requires as many degrees of freedom as the dimension of its scale
matrix, so n1 + n2 - 2 = 1 failed inside it. The Wishart
matrix is the outer product of a single normal draw there, and only its
diagonal enters the calculation, so that case is drawn
directly.
The bivariate normal distribution function is no longer evaluated
at arguments it cannot handle. A standardized effect of several hundred,
which a small standard deviation produces, sends an argument far enough
into a tail that pbivnorm() returns NaN, and
the reported co-primary power was not a number. The arguments are held
at eight standard deviations, beyond which the normal distribution
function is zero or one to within 1e-15.
The co-primary power is held inside the interval that its two
marginal powers allow, in every power function that evaluates a
bivariate normal distribution function. Rounding could otherwise return
a value a few times 1e-19 below zero, and in
power2Continuous(known_var = FALSE), where the marginals
are exact and the joint probability is simulated, a small
nMC could put the simulated value above the smaller
marginal.
ss1Continuous(), ss1Count() and
ss1BinaryApprox() return at least one subject per group.
Their closed forms give zero when the target power does not exceed the
size of the test, at alpha of 0.1 and beta of
0.9 for instance, and ss1BinaryApprox() then evaluated its
power at a group of no patients.
The two-endpoint sample size functions are unaffected by the
ss1BinaryApprox() corrections, because they use it only as
the starting value for a sequential search that converges to the minimum
sample size from any starting point.
ss2MixedCountContinuous() evaluates the correlation
bounds once instead of twice at every step of its sequential search. The
bounds are a quadrature over the support of the negative binomial
distribution and depend only on the parameters held fixed by the search.
A search at the default settings takes about 0.2 seconds rather than
about 2.7.twoCoprimary2BinaryExact() documented
Test = "Z-pooled", which the code rejects, and omitted
"Fisher-midP", which it accepts.design_table() now documents the five exact test
methods it dispatches on.power2MixedContinuousBinary() documents the
nMC column it returns.power2MixedCountContinuous() writes the test statistics
and the correlation between them in the indexing used by the package,
group 1 for treatment and group 2 for control, rather than the indexing
of the source article, and states that the event rates r1
and r2 are distinct from the allocation ratio
r. The variance component V_a is now defined
where it is used.ss2MixedCountContinuous() writes the mean count as
lambda_j = r_j * t.ss1BinaryApprox() documents the requirement that
p1 exceed p2, and no longer describes a
binomial calculation as hypergeometric. Its arcsine formula matches the
implementation.plot() documents the endpoint-specific default for
rho_range and the cost of n_points for exact
and Monte Carlo based objects.ss1Count() documents that r1 must be less
than r2.plot() documents that the "effect_contour"
axes are standardized effect sizes.mixed-count-continuous is
written with the event rates rather than the mean counts, which is the
form of equation 8 of Homma and Yoshida (2024) and the form the code
uses; its Case B design parameters name the treatment and control rates
in the order the code passes them. The non-centrality parameter in
two-continuous-endpoints is written with the standardized
effect size. mixed-continuous-binary states the allocation
ratio r of the package alongside the kappa of
Sozu et al. (2012), uses the upper-tail quantile in the power formula
and its two critical values, closes the parenthesis in the latent normal
distribution, and no longer writes the standardized statistic of the
continuous endpoint in terms of proportions. overview
separates the patient-level correlation the user supplies from the
correlation between test statistics that enters the power formula.
two-binary-endpoints-exact writes the null and alternative
hypotheses with the subscripts used by the other vignettes, and denotes
the multinomial cell counts by N rather than by
Z, which is the test statistic elsewhere.two-binary-endpoints-exact, the grid sizes at which the
rejection regions were compared in the same vignette, and how many of
the published Fisher sample sizes the test suite checks.rr1Binary() now gives every outcome in a tie group
the same p-value for the two exact unconditional tests,
"Z-pool" and "Boschloo". The tail event of
such a test is the set of outcomes at least as extreme as the observed
one, so outcomes sharing the same value of the ordering statistic must
share a tail probability. A plain cumulative sum gave the earlier
members of a group a smaller p-value, and which member came first
depended on the order that order() happened to return. The
rejection region could therefore be larger than the standard test’s, and
the result was not reproducible. The corrected rejection regions agree
with those implied by the Exact package at
alpha = 0.01, 0.025 and 0.05 for both tests.
This changes one entry of Table 4 of Homma and Yoshida (2025): for
the Z-pooled test with alpha = 0.05, r = 2 and
rho = 0.3 the required total sample size is 147 rather than
the published 144. The remaining 95 entries of that table, and every
design behind its Figures 1 to 3 but one, are unchanged.
power2Continuous() with
known_var = FALSE now draws the Wishart matrix from the
correlation matrix of the standardized endpoints rather than from the
variance-covariance matrix. The test statistic is already divided by
sd1 and sd2, so a factor of the standard
deviation was left in the critical value and canceled only when
sd1 = sd2 = 1. Power is now invariant to a common rescaling
of the effects and the standard deviations, as it must be, and agrees
with a direct simulation of the trial.
power2MixedContinuousBinary() with
Test = "Fisher" now returns the simulated result. The block
computing the asymptotic result was not inside an else, so
it ran for every value of Test and overwrote what the
Fisher branch had computed; a request for "Fisher" returned
the "ASc" value. The latent binary variable is also now
centered in both groups and dichotomized at a group specific threshold,
following Sozu et al. (2012). Both groups had previously been
dichotomized at a single threshold, which pinned the control response
probability at 0.5 whatever p2 was and reversed the
direction of the effect. The corrected implementation reproduces all 24
Fisher entries of Table S5 in the Supporting Information of Sozu et
al. (2012) to within Monte Carlo error.
The co-primary power in power2BinaryExact() is now
evaluated as two matrix products of order n + 1 instead of
forming two matrices of order K, the number of outcomes in
the rejection region. Since K grows like n ^ 2
the cost fell from order n ^ 4 to order n ^ 3
in both time and memory. At n1 = n2 = 200 the previous
expression required about 4 GB and could not be evaluated on a typical
machine.
The conditional probability of the bivariate binomial
distribution used by dbibinom() is now computed in C++. The
powers and binomial coefficients that the sum needs are tabulated once,
which reduces the number of calls to pow and
choose from order N ^ 3 to order
N ^ 2. Building one probability mass matrix at
N = 200 takes about 0.07 seconds rather than 2.1
seconds.
Together these make a sample size search for two binary endpoints with exact methods around four times faster at moderate sample sizes, and possible at all at large ones.
rr1Binary(), power2BinaryExact(),
ss2BinaryExact(), twoCoprimary2BinaryExact()
and design_table() gain an n_grid argument
giving the number of points at which the null tail probability is
maximized over the nuisance parameter in the two exact unconditional
tests. The value was previously fixed at 100 internally, which remains
the default, so existing results are reproduced exactly. Values below 10
are rejected, since a coarse grid can miss the maximum and return an
anti-conservative p-value.power2Continuous(),
power2MixedContinuousBinary() and
ss2MixedContinuousBinary() now state that their Monte Carlo
branches draw random numbers and that a seed should be set for
reproducible results.
rr1Binary() documents how tied outcomes are
handled.
Rcpp is a new dependency, in Imports
and LinkingTo.
Test coverage was extended with invariance checks that apply
across all five endpoint type combinations: the co-primary power
factorizes into the product of the marginal powers at zero correlation,
power depends on a continuous endpoint only through its standardized
effect, and the returned sample size is the smallest one reaching the
target. The exact unconditional tests are also checked against the
Exact package where it is installed.
A spelling check was added (tests/spelling.R with
inst/WORDLIST), so the British and American spelling
inconsistencies corrected in this version cannot reappear
unnoticed.
This is the first release of twoCoprimary, providing comprehensive tools for sample size and power calculation in clinical trials with two co-primary endpoints.
ss2Continuous(), power2Continuous(),
twoCoprimary2Continuous()ss2BinaryApprox(), power2BinaryApprox(),
twoCoprimary2BinaryApprox()ss2BinaryExact(), power2BinaryExact(),
twoCoprimary2BinaryExact()ss2MixedContinuousBinary(),
power2MixedContinuousBinary(),
twoCoprimary2MixedContinuousBinary()ss2MixedCountContinuous(),
power2MixedCountContinuous(),
twoCoprimary2MixedCountContinuous()corrbound2Binary() - Calculate valid correlation bounds
for binary endpointscorrbound2MixedCountContinuous() - Calculate valid
correlation bounds for count and continuous endpointsdesign_table() - Create comprehensive design comparison
tablesplot.twoCoprimary() - Visualize sample size vs
correlation relationships
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